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 A156603 A q-factorial triangle sequence built of Cartan A_n polynomials as antidiagonals: p(x,n)=CartanAn(x,n): t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]]; 0
 1, 1, 1, 1, 1, 2, 1, 1, 0, 6, 1, 1, -1, 0, 24, 1, 1, -2, 0, 0, 120, 1, 1, -3, -6, 0, 0, 720, 1, 1, -4, -24, 24, 0, 0, 5040, 1, 1, -5, -60, 504, 120, 0, 0, 40320, 1, 1, -6, -120, 3360, 27720, -720, 0, 0, 362880, 1, 1, -7, -210, 13800, 702240, -3991680, -5040, 0, 0, 3628800 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums are: {1, 2, 4, 8, 25, 120, 713, 5038, 40881, 393116, 347905,...}. LINKS FORMULA p(x,n)=CartanAn(x,n): t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]]; Out_(n,m)=antidiagonal(t(n,m)). EXAMPLE {1}, {1, 1}, {1, 1, 2}, {1, 1, 0, 6}, {1, 1, -1, 0, 24}, {1, 1, -2, 0, 0, 120}, {1, 1, -3, -6, 0, 0, 720}, {1, 1, -4, -24, 24, 0, 0, 5040}, {1, 1, -5, -60, 504, 120, 0, 0, 40320}, {1, 1, -6, -120, 3360, 27720, -720, 0, 0, 362880}, {1, 1, -7, -210, 13800, 702240, -3991680, -5040, 0, 0, 3628800} MATHEMATICA Clear[t, n, m, i, k, a, b, T, M, p]; T[n_, m_, d_] := If[ n == m, 2, If[n == m - 1 || n == m + 1, -1, 0]]; M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; p[x_, n_] := If[n == 0, 1, CharacteristicPolynomial[M[n], x]]; a0 = Table[p[x, n], {n, 0, 20}] /. x -> m + 1; t[n_, m_] = If[m == 0, n!, Product[a0[[k]], {k, 1, n}]]; a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}]; b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}]' Flatten[%] CROSSREFS Sequence in context: A064879 A173591 A343320 * A156612 A342645 A096801 Adjacent sequences:  A156600 A156601 A156602 * A156604 A156605 A156606 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 11 2009 STATUS approved

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Last modified May 13 22:47 EDT 2021. Contains 343868 sequences. (Running on oeis4.)